Determination of the dynamic elastic modulus of rock samples using various methods of laser ultrasound diagnostics

The main elastic parameter of geomechanical models is the modulus of elasticity. When there is no sufficient amount of geological material (rock core), dynamic elastic moduli are determined using known models; the static moduli are evaluated using dynamic ones. Existing ultrasonic techniques that involve generating and recording ultrasound with piezoelectric components are unable to measure velocities with high accuracy. To address this problem, it is proposed to use laser ultrasonic diagnostics. In this work, we examined full-size rock samples of different genotypes: granite and limestone. The dynamic elastic moduli of full-size granite and limestone specimens are determined from elastic wave velocities measured with a Geoscan02MU laser ultrasonic detector operating in a through-transmission mode. The moduli of thin plate-like specimens prepared from full-size granite and limestone samples were determined using a UDL-2M detector operating in a pulse-echo mode. The dynamic elastic moduli of fullsize specimens and plate-like specimens were compared. Correlation and regression analysis shows that there is a close relationship between the dynamic elastic moduli of full-size specimens and plate-like specimens. It is found that the dynamic modulus of elasticity of rocks can be evaluated using a thin plate-like specimens prepared from undisturbed core. Also, an algorithm is developed for the preliminary assessment of the dynamic modulus of elasticity of rocks using thin plate-like specimens.

Shibaev I. A. Determination of the dynamic elastic modulus of rock samples using various methods of laser ultrasound diagnostics. MIAB. Mining Inf. Anal. Bull. 2021;(4-1):138—147. [In Russ]. DOI: 10.25018/0236_1493_2021_41_0_138.

The reported study was funded by RFBR, project number 19-35-90063.

Shibaev I. A., PhD-student, mrdfyz@mail.ru, National Research Technological University “MISiS” Mining Institute, Moscow, Russia.

1. Osipov Yu. V., Koshelev A. E. Modern methods for determining the deformation properties of rocks. Mining informational and analytical bulletin. 2017, no. 11, pp. 68—75. DOI: 10.25018/0236-1493-2017-11-0-68-75 [In Russ].

2. Eissa E. A., Kazi A. Relation between static and dynamic Young’s moduli of rocks. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1988, Vol. 25, Issue 6, pp. 479—482.

3. Wellington S. L., Vinegar H. J. X-ray computerized tomography. Journal of Petroleum Technology, 1987, no 39, pp. 885–898. DOI: http://dx.doi.org/10.2118/16983-PA.

4. Ketcham R. A., Carlson W. D. Acquisition, optimization and interpretation of X-ray computed tomographic imagery: Applications to the geosciences. Computers & Geosciences, 2001, Issue 27, pp. 381—400. DOI: http://dx.doi.org/10.1016/S0098—3004(00)00116—3.

5. Koopialipoor M., no.orbakhsh A., Ghaleini E. N., Armaghani D. J., Yagiz S. A new approach for estimation of rock brittleness based on non-destructive tests. no.ndestructive Testing and Evaluation, 2019, Vol. 34, Issue 4, pp. 354— 375. DOI: 10.1080/10589759.2019.1623214.

6. Shibaev I. A., Vinnikov V. A., Stepanov G. D. Determination of the elastic properties of sedimentary rocks on the example of limestone samples using laser ultrasound diagnostics. Mining informational and analytical bulletin. 2020, no 7, pp. 125—134. DOI: 10.25018/0236-1493-2020-7-0-125-134. [In Russ].

7. Mashinsky E. I. Physical reasons for the difference in the static and dynamic elastic modulus of rocks. Geology and Geophysics. 2003, volume 44. no 9, pp. 953—959. [In Russ].

8. Auld B. A. Acoustic Fields and Waves in Solids. Volume 1. Krieger Publishing Company California, 1990, 446 p.

9. Porody gornyye. Metod opredeleniya skorostey uprugikh prodol’nykh i poperechnykh voln, GOST 21153.7—75. [Rocks. Method for determining the propagation velocities of elastic longitudinal and transverse waves, State Standart 21153.7—75], Moscow, Standarty, 1981, 7 p. [In Russ].

10. ASTM 2845—08. Standard Test Method for Laboratory Determination of Pulse Velocities and Ultrasonic Elastic Constants of Rock, 2017, 7 pages.

11. In’kov V. N., Cherepetskaya E. B., Shkuratnik V. L., Karabutov A. A., Makarov V. A. Ultrasonic echo sounding by thermal optical sources of longitudinal waves. Journal of Mining Science, 2004, Volume 40, Issue 3, pp. 231—235.

12. Bychkov A., Simonova V., Zarubin V., Cherepetskaya E., Karabutov A. The progress in photoacoustic and laser ultrasonic tomographic imaging for biomedicine and industry: A review. Applied Sciences, 2018, Volume 8, Issue 10, Article 1931. DOI:10.3390/app8101931.

13. Cherepetskaya E. B., Karabutov A. A., Makarov V. A., Mironova E. A., Shibaev I. A., Vysotin N. G., Morozov D. V., Internal structure research of shungite by broadband ultrasonic spectroscopy. Key Engineering Materials, 2017, Volume 755, pp. 242—247

14. Grigoriev K. S., Kuznetsov N. Yu., Cherepetskaya E. B., Makarov V. A. Second harmonic generation in isotropic chiral medium with nonlocality of nonlinear optical response by heterogeneously polarized pulsed beams. Optics Express, 2017, Vol 25, Issue 6, pp. 6253—6262. DOI: 10.1364/OE.25.006253

15. Bychkov A. S., Cherepetskaya E. B., Karabutov A. A., Makarov V. A. Laser optoacoustic tomography for the study of femtosecond laser filaments in air. Laser Physics Letters, 2016, Vol. 13, no. 8, pp. 085401—085405. DOI: 10.1088/1612-2011/13/8/085401

16. Kravtsov A., Ivanov P. N., Malinnikova O. N., Cherepetskaya Е. B., Gapeev A. A. Laser–ultrasonic spectroscopy of the Pechora basin coal microstructure. MIAB. Mining Inf. Anal. Bull. 2019, Vol. 6, pp. 56—65. [In Russ]. DOI: 10.25018/0236-1493-2019-06-056-65 [In Russ].

17. Favorskaya A. V., Investigation of plate material properties by laser ultrasound using multiple wave analysis. Computernie issledovaniya i modelirovanie, 2019, Vol. 11, Issue. 4, pp. 653—673 [In Russ].